
TIGRE

Ander Biguri, Manjit Dosanjh, Steven Hancock and Manuchehr Soleimani
TIGRE: A MATLAB-GPU toolbox for CBCT image reconstruction 
Biomedical Physics & Engineering Express, 2(5):055010 ,2016

@article{TIGRE,
  author={Ander Biguri and Manjit Dosanjh and Steven Hancock and Manuchehr Soleimani},
  title={TIGRE: a MATLAB-GPU toolbox for CBCT image reconstruction},
  journal={Biomedical Physics & Engineering Express},
  volume={2},
  number={5},
  pages={055010},
  url={http://stacks.iop.org/2057-1976/2/i=5/a=055010},
  year={2016},
  abstract={In this article the Tomographic Iterative GPU-based Reconstruction (TIGRE) Toolbox, a MATLAB/CUDA toolbox for fast and accurate 3D x-ray image reconstruction, is presented. One of the key features is the implementation of a wide variety of iterative algorithms as well as FDK, including a range of algorithms in the SART family, the Krylov subspace family and a range of methods using total variation regularization. Additionally, the toolbox has GPU-accelerated projection and back projection using the latest techniques and it has a modular design that facilitates the implementation of new algorithms. We present an overview of the structure and techniques used in the creation of the toolbox, together with two usage examples. The TIGRE Toolbox is released under an open source licence, encouraging people to contribute.}
}
	

ASD_POCS

E.Y. Sidky and X. Pan. 
Image reconstruction in circular cone-beam computed tomography by constrained, total-variation minimization. 
Physics in Medicine and Biology, 53(17):4777, 2008.
DOI: 10.1088/0031-9155/53/17/021

@article{ASD_POCS,
  author={Sidky, E.Y. and Pan, X.},
  title={Image reconstruction in circular cone-beam computed tomography by constrained, total-variation minimization},
  journal={Physics in Medicine and Biology},
  volume={53},
  number={17},
  pages={4777},
  url={http://stacks.iop.org/0031-9155/53/i=17/a=021},
  year={2008},
  abstract={An iterative algorithm, based on recent work in compressive sensing, is developed for volume image reconstruction from a circular cone-beam scan. The algorithm minimizes the total variation (TV) of the image subject to the constraint that the estimated projection data is within a specified tolerance of the available data and that the values of the volume image are non-negative. The constraints are enforced by the use of projection onto convex sets (POCS) and the TV objective is minimized by steepest descent with an adaptive step-size. The algorithm is referred to as adaptive-steepest-descent-POCS (ASD-POCS). It appears to be robust against cone-beam artifacts, and may be particularly useful when the angular range is limited or when the angular sampling rate is low. The ASD-POCS algorithm is tested with the Defrise disk and jaw computerized phantoms. Some comparisons are performed with the POCS and expectation-maximization (EM) algorithms. Although the algorithm is presented in the context of circular cone-beam image reconstruction, it can also be applied to scanning geometries involving other x-ray source trajectories.}
}

B_ASD_POCS_beta

H. Xue, L. Zhang, Z. Cheng, Y. Xing and Y. Xiao. 
An improved tv minimization algorithm for incomplete data problem in computer tomography. 
Nuclear Science Symposium Conference Record (NSS/MIC), 2010 IEEE, pages 2621-2624, Oct 2010
DOI: 10.1109/NSSMIC.2010.5874264

@INPROCEEDINGS{B_ASD_POCS_beta, 
author={H. Xue and L. Zhang and Z. Cheng and Y. Xing and Y. Xiao}, 
booktitle={Nuclear Science Symposium Conference Record (NSS/MIC), 2010 IEEE}, 
title={An improved TV minimization algorithm for incomplete data problem in computer tomography}, 
year={2010}, 
pages={2621-2624}, 
keywords={computerised tomography;image reconstruction;iterative methods;medical image processing;minimisation;B-POCS-TV-$\beta$;Bregman iteration;POCS-TV method;TV minimization algorithm;computer tomography;convergence speed;image quality;incomplete data problem;reconstruction error;total variation;Computed tomography;Convergence;Image reconstruction;Minimization;Optimization;TV;B-POCS-TV-$\beta$;Computer tomography (CT);POCS-TV;TV minimization;few-view;limited-angle}, 
doi={10.1109/NSSMIC.2010.5874264}, 
ISSN={1095-7863}, 
month={Oct}
}

CGLS

Ake Bjorck
Numerical Methods for Least Squares Problems
Society for Industrial and Applied Mathematics, 1996
DOI: 10.1137/1.9781611971484

@book{doi:10.1137/1.9781611971484,
author = {Bjorck, A.},
title = {Numerical Methods for Least Squares Problems},
publisher = {Society for Industrial and Applied Mathematics},
year = {1996},
doi = {10.1137/1.9781611971484},
address = {},
edition   = {},
URL = {http://epubs.siam.org/doi/abs/10.1137/1.9781611971484},
eprint = {http://epubs.siam.org/doi/pdf/10.1137/1.9781611971484}
}

FDK

L.A. Feldkamp, L.C. Davis and J.W. Kress. 
Practical cone-beam algorithm. 
J. Opt.Soc. Am. A, 1(6):612{619, Jun 1984.
DOI: 10.1364/JOSAA.1.000612

@article{FDK, 
author = {L.A. Feldkamp and L.C. Davis and J.W. Kress}, 
journal = {J. Opt. Soc. Am. A}, 
keywords = {},
number = {6}, 
pages = {612--619}, 
publisher = {OSA},
title = {Practical cone-beam algorithm}, 
volume = {1}, 
month = {Jun},
year = {1984},
url = {http://josaa.osa.org/abstract.cfm?URI=josaa-1-6-612},
doi = {10.1364/JOSAA.1.000612},
abstract = {A convolution-backprojection formula is deduced for direct reconstruction of a three-dimensional density function from a set of two-dimensional projections. The formula is approximate but has useful properties, including errors that are relatively small in many practical instances and a form that leads to convenient computation. It reduces to the standard fan-beam formula in the plane that is perpendicular to the axis of rotation and contains the point source. The algorithm is applied to a mathematical phantom as an example of its performance.},
}

OS_SART

Y. Censor and T. Elfving. 
Block-iterative algorithms with diagonally scaled oblique projections for the linear feasibility problem. 
SIAM Journal on Matrix Analysis and Applications, 24(1):40-58, 2002.
DOI: 10.1137/S089547980138705X

@article{OS_SART,
author = {Y. Censor and T. Elfving},
title = {Block-Iterative Algorithms with Diagonally Scaled Oblique Projections for the Linear Feasibility Problem},
journal = {SIAM Journal on Matrix Analysis and Applications},
volume = {24},
number = {1},
pages = {40-58},
year = {2002},
doi = {10.1137/S089547980138705X},
URL = { http://dx.doi.org/10.1137/S089547980138705X},
eprint = {  http://dx.doi.org/10.1137/S089547980138705X}
}

OS_ASD_POCS

E.Y. Sidky and X. Pan. 
Image reconstruction in circular cone-beam computed tomography by constrained, total-variation minimization. 
Physics in Medicine and Biology, 53(17):4777, 2008.
DOI: 10.1088/0031-9155/53/17/021

@article{ASD_POCS,
  author={Sidky, E.Y. and Pan, X.},
  title={Image reconstruction in circular cone-beam computed tomography by constrained, total-variation minimization},
  journal={Physics in Medicine and Biology},
  volume={53},
  number={17},
  pages={4777},
  url={http://stacks.iop.org/0031-9155/53/i=17/a=021},
  year={2008},
  abstract={An iterative algorithm, based on recent work in compressive sensing, is developed for volume image reconstruction from a circular cone-beam scan. The algorithm minimizes the total variation (TV) of the image subject to the constraint that the estimated projection data is within a specified tolerance of the available data and that the values of the volume image are non-negative. The constraints are enforced by the use of projection onto convex sets (POCS) and the TV objective is minimized by steepest descent with an adaptive step-size. The algorithm is referred to as adaptive-steepest-descent-POCS (ASD-POCS). It appears to be robust against cone-beam artifacts, and may be particularly useful when the angular range is limited or when the angular sampling rate is low. The ASD-POCS algorithm is tested with the Defrise disk and jaw computerized phantoms. Some comparisons are performed with the POCS and expectation-maximization (EM) algorithms. Although the algorithm is presented in the context of circular cone-beam image reconstruction, it can also be applied to scanning geometries involving other x-ray source trajectories.}
}

SART

A. H. Andersen and A. C. Kak. 
Simultaneous algebraic reconstruction technique(SART): a superior implementation of the ART algorithm. 
Ultrasonic imaging, 6(1):81-94, 1984
DOI: 10.1016/0161-7346(84)90008-7
@article{SART,
  title={Simultaneous algebraic reconstruction technique ({SART}): a superior implementation of the {ART} algorithm},
  author={Andersen, A.H. and Kak, A.C.},
  journal={Ultrasonic imaging},
  volume={6},
  number={1},
  pages={81--94},
  year={1984},
  publisher={SAGE Publications}
}


SART_TV

Ander Biguri
Iterative recosntruction and motion compensation in computed tomography on GPUs,
PhD thesis, Nov 2017.

@phdthesis{SART_TV,
  author       = {Ander Biguri}, 
  title        = {Iterative recosntruction and motion compensation in computed tomography on {GPU}s},
  school       = {University of Bath},
  year         = 2017,
  address      = {Bath, UK},
  month        = 11
}

SIRT

A. C. Kak and Malcolm Slaney
Principles of Computerized Tomographic Imaging
Society of Industrial and Applied Mathematics, 2001.
DOI: 10.1137/1.9780898719277

@book{SIRT,
   title = "Principles of computerized tomographic imaging",
   author = "Kak, Avinash C. and Slaney, Malcolm and IEEE Engineering in Medicine and Biology Society",
   publisher = "IEEE Press",
   address = "New York",
   url = "http://opac.inria.fr/record=b1086573",
   isbn = "0-87942-198-3",
   note = "Published under the sponsorship of the IEEE Engineering in Medicine and Biology Society.",
   year = 1988
}


sheppLogan3D

If the 'yu-ye-wang' option is used:

Hengyong Yu, Yangbo Ye and Ge Wang 
Katsevich-type algorithms for variable radius spiral cone-beam CT
Proceedings of SPIE - The International Society for Optical Engineering. 10/2004; 5535:550-557. 
DOI: 10.1117/12.559300

@inproceedings{sheppLogan3D,
  title={Katsevich-type algorithims for variable radius spiral cone-beam CT},
  author={Yu, Hengyong and Ye, Yangbo and Wang, Ge},
  booktitle={Optical Science and Technology, the SPIE 49th Annual Meeting},
  pages={550--557},
  year={2004},
  organization={International Society for Optics and Photonics}
}

phantom3dAniso

If the 'yu-ye-wang' option is used:

Hengyong Yu, Yangbo Ye and Ge Wang 
Katsevich-type algorithms for variable radius spiral cone-beam CT
Proceedings of SPIE - The International Society for Optical Engineering. 10/2004; 5535:550-557. 
DOI: 10.1117/12.559300

@inproceedings{sheppLogan3D,
  title={Katsevich-type algorithims for variable radius spiral cone-beam CT},
  author={Yu, Hengyong and Ye, Yangbo and Wang, Ge},
  booktitle={Optical Science and Technology, the SPIE 49th Annual Meeting},
  pages={550--557},
  year={2004},
  organization={International Society for Optics and Photonics}
}

Measure_Quality

Please refer to the individual parameters used instead of the function itself

@notabib{
Please refer to the individual parameters used instead of the function itself
}



RMSE

J-H Kim,J Nuyts,A Kyme,Z Kuncic and R Fulton
A rigid motion correction method for helical computed tomography (CT)
Physics in Medicine & Biology, Phys. Med. Biol. 60 (2015) 2047�2073
DOI:10.1088/0031-9155/60/5/2047 

@article{kim2015rigid,
  title={A rigid motion correction method for helical computed tomography (CT)},
  author={Kim, JH and Nuyts, Johan and Kyme, A and Kuncic, Z and Fulton, R},
  journal={Physics in medicine and biology},
  volume={60},
  number={5},
  pages={2047},
  year={2015},
  publisher={IOP Publishing}
}

CC

J-H Kim,J Nuyts,A Kyme,Z Kuncic and R Fulton
A rigid motion correction method for helical computed tomography (CT)
Physics in Medicine & Biology, Phys. Med. Biol. 60 (2015) 2047�2073
DOI:10.1088/0031-9155/60/5/2047 

@article{kim2015rigid,
  title={A rigid motion correction method for helical computed tomography (CT)},
  author={Kim, JH and Nuyts, Johan and Kyme, A and Kuncic, Z and Fulton, R},
  journal={Physics in medicine and biology},
  volume={60},
  number={5},
  pages={2047},
  year={2015},
  publisher={IOP Publishing}
}

MSSIM

J-H Kim,J Nuyts,A Kyme,Z Kuncic and R Fulton
A rigid motion correction method for helical computed tomography (CT)
Physics in Medicine & Biology, Phys. Med. Biol. 60 (2015) 2047�2073
DOI:10.1088/0031-9155/60/5/2047 

@article{kim2015rigid,
  title={A rigid motion correction method for helical computed tomography (CT)},
  author={Kim, JH and Nuyts, Johan and Kyme, A and Kuncic, Z and Fulton, R},
  journal={Physics in medicine and biology},
  volume={60},
  number={5},
  pages={2047},
  year={2015},
  publisher={IOP Publishing}
}

UQI

Wang, Zhou, and Alan C. Bovik. 
A universal image quality index.
IEEE signal processing letters 9, no. 3 (2002): 81-84.
DOI: 

@article{wang2002universal,
  title={A universal image quality index},
  author={Wang, Zhou and Bovik, Alan C},
  journal={IEEE signal processing letters},
  volume={9},
  number={3},
  pages={81--84},
  year={2002},
  publisher={IEEE}
}

SophiaBeads data

S. B. Coban and S. A. McDonald
SophiaBeads Dataset Project. 
Zenodo (2015)  
DOI: http://dx.doi.org/10.5281/zenodo.16474.

@misc{coban_2015_16474,
  author       = {Coban, S. B. and
                  McDonald, S. A.},
  title        = {SophiaBeads Dataset Project},
  month        = mar,
  year         = 2015,
  doi          = {10.5281/zenodo.16474},
  url          = {http://dx.doi.org/10.5281/zenodo.16474}
}

SophiaBeads code

S. B. Coban 
SophiaBeads Dataset Project Codes 
Zenodo (2015)  
DOI: http://dx.doi.org/10.5281/zenodo.16539

@misc{coban_2015_16539,
  author       = {Coban, S. B.},
  title        = {SophiaBeads Dataset Project Codes},
  month        = apr,
  year         = 2015,
  doi          = {10.5281/zenodo.16539},
  url          = {http://dx.doi.org/10.5281/zenodo.16539}
}

MLEM

J. M. Ollinger
Maximum-likelihood reconstruction of transmission images in emission computed tomography via the EM algorithm
IEEE Transactions on Medical Imaging, 12 (1994) p89-101
DOI: 10.1109/42.276147

@article{ollinger1994maximum,
  title={Maximum-likelihood reconstruction of transmission images in emission computed tomography via the EM algorithm},
  author={Ollinger, John M},
  journal={IEEE transactions on medical imaging},
  volume={13},
  number={1},
  pages={89--101},
  year={1994},
  publisher={IEEE}
}

headPhantom

A. Aichert, M. Manhart, B. Navalpakkam, R. Grimm, J. Hutter, A. Maier, J. Hornegger, A. Doerfler
A Realistic Digital Phantom for Perfusion C-Arm CT Based on MRI Data
2013 IEEE Nuclear Science Symposium and Medical Imaging Conference Record (NSS/MIC), Seoul, Korea, 2013.

@inproceedings{aichert2013realistic,
  title={A realistic digital phantom for perfusion C-arm CT based on MRI data},
  author={Aichert, Andr{\'e} and Manhart, Michael T and Navalpakkam, Bharath K and Grimm, Robert and Hutter, Jana and Maier, Andreas and Hornegger, Joachim and Doerfler, Arnd},
  booktitle={2013 IEEE Nuclear Science Symposium and Medical Imaging Conference (2013 NSS/MIC)},
  pages={1--2},
  year={2013},
  organization={IEEE}
}

PCSD

L. Liu, W. Lin, M. Jin
Reconstruction of sparse-view X-ray computed tomography using adaptive iterative algorithms
Computers in Biology and Medicine, 56(2015), 97-106
DOI: http://dx.doi.org/10.1016/j.compbiomed.2014.11.001

@article{liu2015reconstruction,
  title={Reconstruction of sparse-view X-ray computed tomography using adaptive iterative algorithms},
  author={Liu, Li and Lin, Weikai and Jin, Mingwu},
  journal={Computers in biology and medicine},
  volume={56},
  pages={97--106},
  year={2015},
  publisher={Elsevier}
}

AwASD-POCS

Y. Liu, J. Ma, Y. Fan,  Z. Liang
Adaptive-weighted total variation minimization for sparse data toward low-dose x-ray computed tomography image reconstruction
Physics in Medicine and Biology, 57(2012), 7923-7956
DOI: 10.1088/0031-9155/57/23/7923

@article{liu2012adaptive,
  title={Adaptive-weighted total variation minimization for sparse data toward low-dose x-ray computed tomography image reconstruction},
  author={Liu, Yan and Ma, Jianhua and Fan, Yi and Liang, Zhengrong},
  journal={Physics in medicine and biology},
  volume={57},
  number={23},
  pages={7923},
  year={2012},
  publisher={IOP Publishing}
} 

AwPCSD

M. Lohvithee, A. Biguri, M. Soleimani
Parameter selection in limited data cone-beam CT reconstruction using edge-preserving total variation algorithms
Physics in Medicine and Biology, 2017

@article{lohvithee2017parameter,
  title={Parameter selection in limited data cone-beam CT reconstruction using edge-preserving total variation algorithms},
  author={Lohvithee, Manasavee and Biguri, Ander and Soleimani, Manuchehr},
  journal={Physics in Medicine and Biology},
  year={2017},
  publisher={IOP Publishing}
}


End of Bib (leave this here)